This invention relates to seismic exploration and more particularly to a method and apparatus for removing sinusoidal noise from seismic data. This invention further relates to method and apparatus for providing an improved notch filter which utilizes an exact mathematical description of sinusoidal noise for application to a noisy seismic trace.
In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus produced is commonly interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismograms are commonly recorded as digital samples representing the amplitude of a received signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. Before an array of seismic samples or traces can be converted into a seismic section for interpretations by geophysicists, the array must be extensively processed to remove noise and to make reflection events discernible.
In the course of seismic exploration, a significant amount of noise is introduced into the seismic data by the influence of man. Such introduced noise, generally referred to as "cultural noise", may include noise from power lines, electrical machinery or other sources. As a result, sinusoidal noise is often a serious problem in analyzing seismic records. However, geophysicists usually ignore the sinusoidal noise or rely upon deconvolving and/or stacking of the seismic data to reduce sinusoidal noise. Unfortunately, sinusoidal noise left on a seismic record degrades subsequent processing techniques such as determining amplitude recovery parameters, source-receiver coupling corrections, source-receiver static corrections, trace editing, deconvolution, multiple removal, and wavelet estimates. However, using deconvolution to simultaneously remove sinusoidal noise and whiten the data leads to relatively poor signal to noise ratios and to signal distortion.
Another method for removing such types of sinusoidal noise contamination is to pass the seismic data through a notch filter. Unfortunately, poor results were often obtained when the removal of contaminating sinusoidal noise was attempted utilizing notch filters. First, the notch may not be centered exactly at the frequency of the contaminating noise, thereby making it more likely that not all of the contaminating noise will be removed by the notch. Second, the notch may remove a considerable amount of valid data along with the noise if the valid data has a frequency within the notch and the notch is wide. Finally, in some cases, the notch filter will induce phase distortion in the data.
Much of the seismic data collected today is contaminated by power-line interference or sinusoidal interference from nearby power generators. Noise from high-voltage transmission lines is considered very stationary and therefore can be effectively removed by notch filtering, provided that a filter with a narrow and deep notch can be utilized. In the past, to construct a notch filter having both a deep and narrow notch required the use of very long filter operators. However, such a practice has been discouraged as the amount of computer time required to apply the long filter operators having a deep and narrow notch is very high, thus adding substantially to the cost of notch filtering the seismic data.